The positive integers x,y, and z are such that x is a factor of y and y is a factor of z. Is z even?
(1) xz is even
(2) y is even
Can someone please help me here...?
Thanks.
GMAT Prep?? (Factors)
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- AleksandrM
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The foundation rule here is that if x is a factor of y and y is a factor of z then x is also a factor of z. Now, you also know that y is bigger than x and z is either bigger than xy or equals to it.
Statement one tells you that xz is even. This means that one of the numbers is even. However, you also know that x is a factor of y. So if x is 3 and y is 9, then z MUST be even, or 18, for example. Sufficient.
Statement two tells you that y is even. If y is 6 and x is any odd integer, when you multiply them together, the result is always even. Now, z can have other factors, and all of them can be odd. As long as one of the factors is even, z MUST be even. Sufficient.
Choose D.
Statement one tells you that xz is even. This means that one of the numbers is even. However, you also know that x is a factor of y. So if x is 3 and y is 9, then z MUST be even, or 18, for example. Sufficient.
Statement two tells you that y is even. If y is 6 and x is any odd integer, when you multiply them together, the result is always even. Now, z can have other factors, and all of them can be odd. As long as one of the factors is even, z MUST be even. Sufficient.
Choose D.
let p and q be 2 constants
question says
p.x = y
q.y = z
q(p.x) = z
qp.x = z
let qp = some constant m
mx = z
now, evaluate the options
1) xz = even
(z/m).z = even
z.z = even * m
z.z = even
therefore z = even. SUFFICIENT
2) y = even
we know, q.y = z, q.even = even
so z = even. SUFFICIENT.
(D)
question says
p.x = y
q.y = z
q(p.x) = z
qp.x = z
let qp = some constant m
mx = z
now, evaluate the options
1) xz = even
(z/m).z = even
z.z = even * m
z.z = even
therefore z = even. SUFFICIENT
2) y = even
we know, q.y = z, q.even = even
so z = even. SUFFICIENT.
(D)